Model Of Transonic Flow Research Articles

Acoustic black and white holes of potential flow in a tube

We propose a new simple model of acoustic black hole in a thin tube, where the difference in the gravitational potential is used to create a transonic flow. The main merit of our transonic flow model is that the Euler equations can be solved analytically. In fact, we can obtain an exact solution to the equation in terms of a height function in the monatomic case $\gamma=5/3$. For arbitrary $\gamma$, we find that it takes a simple form by the near-sonic approximation. Moreover, we obtain two analytic solutions describing a backward wave and a forward wave, from which we can confirm the existence of sonic horizons.

Existence and uniqueness for some equation of a mixed elliptic-hyperbolic type

In the paper, we prove results on existence and uniqueness of weak solutions for closed Dirichlet problem for a transonic flow model, and interior regularity results are also given in the important special case of the Tricomi equation. The method employed consists in variants of the a-b-c integral method of Friedrichs in Sobolev spaces with suitable weights. Particular attention is paid to the problem of attaining results with a minimum of restrictions on the boundary geometry and the form of the type change function.

Influence of divergent section on flow fields and discharge coefficient of ISO 9300 toroidal-throat sonic nozzle

The effect of divergent section of ISO 9300 toroidal-throat nozzle on discharge coefficient was analyzed based on the inviscid transonic flow model and laminar boundary layer theory. A series of numerical simulations were conducted to verify the results of theory, and investigate the effect of divergent section length L and diffuser angle θ operated at different Reynolds numbers. Combined with the numerical results in this study and the experimental data reported by Nakao, it showed the discharge coefficient increases with the rise of diffuser angle θ or the drop of divergent section length L. A lot of new results about the effect of divergent section were obtained. It indicated that the effect of divergent section on discharge coefficient of ISO 9300 toroidal-throat nozzle should be considered when Re<1.1×104. At last, a concept of effective critical flow was proposed to discuss the effect of divergent section on discharge coefficient.

On the nature of the parameter space in the presence of dissipative standing shocks in accretion flows around black holes

The spectral properties of black hole candidates and outflow rates depend crucially on the models of accretion flow, and thus they are interconnected. In a model of transonic flow, the centrifugal barrier forms a shock wave in the accretion disc at a few tens of Schwarzschild radii. The post-shock region (i.e. the region between the shock and the innermost critical point) can act as a Compton cloud as well a reservoir of outgoing jets/outflows. In order to compute the parameter space in which the outflow can form, we use a suitable Mach number relation that can be satisfied at the shock derived in our earlier work in the presence of dissipation and outflows. Assuming three models of accretion flow (i.e. models of vertical equilibrium, conical wedge shape and constant height), we examine the parameter space of the specific energy and the specific angular momentum for dissipative shock with mass loss. In the first two models, we find that the parameter space is reduced as the cooling rate is increased. However, in the case of the constant height model, the parameter space initially increases with the cooling process, but starts to decrease with a further increase in cooling. One common property in all three accretion flow models is that, above a critical amount of cooling, the parameter space disappears completely. This indicates that the spectrally soft states might not have a significant amount of outflows from the accretion disc.

Numerical modeling of two-phase transonic flow

Our work is aimed at the development of numerical method for the modeling of transonic flow of wet steam including condensation/evaporation phase change. We solve a system of PDE’s consisting of Euler or Navier-Stokes equations for the mixture of vapor and liquid droplets and transport equations for the integral parameters describing the droplet size spectra. Numerical method is based on a fractional step technique due to the stiff character of source terms, i.e. we solve separately the set of homogenous PDE’s by the finite volume method and the remaining set of ODE’s either by explicit Runge-Kutta or implicit Euler method. The finite volume method is based on the Lax-Wendroff scheme with conservative artificial dissipation terms for structured grid. We also note result achieved by recently developed finite volume method with VFFC scheme. We discuss numerical results of steady and unsteady two-phase transonic flow in 2D nozzle, 2D and 3D turbine cascade and 2D turbine stage with moving rotor cascade.

A magnetohydrodynamic simulation of pellet ablation in the electrostatic approximation

A magnetohydrodynamic numerical model for hydrogenic pellet ablation in the electrostatic approximation has been developed based on the method of front tracking. The main features of the model are the explicit tracking of interfaces that separate the solid pellet from the ablated gas and the cold, dense and weakly ionized ablation cloud from the highly conducting fusion plasma, a surface ablation model, a kinetic model for the electron heat flux and an equation of state accounting for atomic processes in the ablation cloud. The interaction of the pellet ablation flow with the magnetic field including the J × B Lorentz force is studied here systematically for the first time. The model has also been validated through the comparison with the semi-analytic Transonic Flow model and previous purely hydrodynamic simulations. Contrary to prevailing expectations, the ablation rate is reduced only slightly when the geometry is changed from spherically symmetric to axially symmetric, in the case of purely hydrodynamic models. However, in the magnetohydrodynamic simulations the J × B force funnels the flow into an extended plasma shield, which intercepts the incident plasma heat flux and reduces the ablation rate, depending on the rise time of heat flux seen by the pellet. Shorter ‘warm-up’ times lead to narrower ablation channels, stronger shielding and reduced ablation rates. This new feature implies that pellets traversing strong plasma gradients, as in the edge pedestal region of the ITER plasma, could have significantly lower ablation rates if injected at higher velocity.

Numerical Solution of Transonic Turbulent and Two‐phase flow in Turbine cascades

AbstractPresented model of transonic flow with condensation is based on Navier‐Stokes equations for mixture, algebraic turbulence model and Hill's approximation for the description of liquid phase [2]. Two finite volume methods are introduced. Numerical results for single‐phase 2D flow of air in turbine cascade SE1050, two‐phase 2D flow in Laval nozzle and two‐phase 2D flow in turbine cascade SE1050 are presented.

A regularization for a simple model of transonic flow

A regularization for a simple model of transonic flow